A father builds a swing for his children. The swing consists of a board attached to two ropes, as shown in Figure 3.17. The swing is mounted on a tree branch, with the board 3.5 m below the branch. The diameter of the branch is 8.2 cm and the kinetic coefficient of friction between the ropes and the branch is 0.1. After the swing is installed and his child is seated, the father pulls the swing back 10 and releases. What is the decrease in angle of each swing and how many swings will the child receive before Dad needs to give another push?

A father builds a swing for his children. The swing consists of a board attached to two ropes, as shown in Figure 3.17. The swing is mounted on a tree branch, with the board 3.5 m below the branch. The diameter of the branch is 8.2 cm and the kinetic coefficient of friction between the ropes and the branch is 0.1. After the swing is installed and his child is seated, the father pulls the swing back 10 and releases. What is the decrease in angle of each swing and how many swings will the child receive before Dad needs to give another push?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

Question

(a)
T, = T,eHB
H = 0.1
- d = 8.2 cm
3.5 m
T
27
272
FIGURE 3.17
(a) Tree swing of Example 3.11. (b) The tension
developed in opposite sides of a rope are
unequal due to friction. (c) FBDS of swing at an
arbitrary instant.
mg
External forces
Effective forces

A father builds a swing for his children. The swing consists of a board
attached to two ropes, as shown in Figure 3.17. The swing is mounted on a tree
branch, with the board 3.5 m below the branch. The diameter of the branch is 8.2
cm and the kinetic coefficient of friction between the ropes and the branch is 0.1.
After the swing is installed and his child is seated, the father pulls the swing back
10 and releases. What is the decrease in angle of each swing and how many
swings will the child receive before Dad needs to give another push?

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